# Video Lectures

A locally testable code (LTC) is an error correcting code that admits a very efficient membership test. The tester reads a constant number of (randomly - but not necessarily uniformly - chosen) bits from a given word and rejects words with...

Despite the fact that the 3-body problem is an ancient conundrum that goes back to Newton, it is remarkably poorly understood, and is still a benchmark for modern developments. In this talk, I will give a (very) biased account of this classical...

A locally testable code (LTC) is an error correcting code that admits a very efficient membership test. The tester reads a constant number of (randomly - but not necessarily uniformly - chosen) bits from a given word and rejects words with...

In various areas of mathematics there exist "big fiber theorems", these are theorems of the following type: "For any map in a certain class, there exists a 'big' fiber", where the class of maps and the notion of size changes from case to case.

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After surveying some important consequences of the property of bounded generation (BG) dealing with SS-rigidity, the congruence subgroup problem, etc., we will focus on examples of boundedly generated groups. We will prove that every unimodular (n×n...

A fundamental problem in the theory of compressible fluid is to provide a precise description of shock formation and development from smooth initial data. In this talk, I will present recent work in collaboration with Drivas, Shkoller and Vicol on...

A random point process is said to be determinantal if finite subset probabilities correspond to principal minors of some matrix. Determinantal point processes (DPPs) appear in a wide variety of settings, from random matrix theory to combinatorics...

30 years ago I proved that any tight contact structure on the 3-sphere is diffeomorphic to the standard one. I also optimistically claimed at the same paper that similar methods could be used to prove a multi-parametric version: the space of tight...

What does the spectrum of a random matrix look like when we make no assumption whatsoever about the covariance pattern of its entries? It may appear hopeless that anything useful can be said at this level of generality. Nonetheless, a widely used...